Finite Group Databasebeta

← AGL(1,𝔽5)×C13⋊#3862 #50303942

Subgroups — AGL(1,𝔽5)×C13⋊#3862 #50303942

Order 38220.

120 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×C13⋊#3862C211yesmaximal, characteristic
2C72×C13×AGL(1,𝔽5)C311yesmaximal, characteristic, complemented, Hall
3C5×C13⋊#3862C411yescharacteristic, complemented, Hall
4C4×C13⋊#3862—51nomaximal, Hall
5C72×D5×C13C2×C311yescharacteristic
6AGL(1,𝔽5)×#63271—71nomaximal
7AGL(1,𝔽5)×#63270—71nomaximal
8C2×C13⋊#3862—51no—
9C5×C72×C13C3×C411yescharacteristic, complemented, Hall
10AGL(1,𝔽5)×#3862—131nomaximal, Hall
11D5×#63271—71no—
12D5×#63270—71no—
13C4×C72×C13—51noHall
14C13⋊#3862AGL(1,𝔽5)11yescharacteristic, direct product factor, Hall
15C7×C13×AGL(1,𝔽5)—32no—
16C7×C13×AGL(1,𝔽5)ΓL(1,𝔽8)11yescharacteristic, complemented
17C7×C13×AGL(1,𝔽5)ΓL(1,𝔽8)11yescharacteristic, complemented
18D5×#3862—131no—
19C5×#63270—71no—
20C5×#63271—71no—
21C2×C72×C13—51no—
22C4×#63271—351no—
23C4×#63270—351no—
24C72×AGL(1,𝔽5)C13⋊C311yescharacteristic, complemented, Hall
25C7×D5×C13—32no—
26C7×D5×C13C2×ΓL(1,𝔽8)11yescharacteristic
27C7×D5×C13C2×ΓL(1,𝔽8)11yescharacteristic
28AGL(1,𝔽5)×C13⋊C3—491noHall
29C5×#3862—131noHall
30C72×C13C3×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
31C4×#3862—651noHall
32C2×#63271—351no—
33C2×#63270—351no—
34C72×D5C2×C13⋊C311yescharacteristic
35C5×C7×C13—32no—
36C5×C7×C13C4×ΓL(1,𝔽8)11yescharacteristic, complemented
37C5×C7×C13C4×ΓL(1,𝔽8)11yescharacteristic, complemented
38AGL(1,𝔽5)×ΓL(1,𝔽8)—911no—
39AGL(1,𝔽5)×ΓL(1,𝔽8)—911no—
40D5×C13⋊C3—491no—
41C4×C7×C13—51no—
42C4×C7×C13—51no—
43C4×C7×C13—152no—
44C2×#3862—651no—
45#63271—71no—
46#63270—71no—
47C13×AGL(1,𝔽5)#386211yescharacteristic, complemented, Hall
48C5×C72C4×C13⋊C311yescharacteristic, complemented, Hall
49D5×ΓL(1,𝔽8)—911no—
50D5×ΓL(1,𝔽8)—911no—
51C4×C72—51noHall
52C5×C13⋊C3—491noHall
53C2×C7×C13—51no—
54C2×C7×C13—51no—
55C2×C7×C13—152no—
56C4×C13⋊C3—2451noHall
57#3862—131noHall
58C7×AGL(1,𝔽5)—32no—
59C7×AGL(1,𝔽5)#6327011yescharacteristic, complemented
60C7×AGL(1,𝔽5)#6327111yescharacteristic, complemented
61D5×C13C2×#386211yescharacteristic
62C5×ΓL(1,𝔽8)—911no—
63C5×ΓL(1,𝔽8)—911no—
64C2×C72—51no—
65C7×C13—32no—
66C7×C13AGL(1,𝔽5)×ΓL(1,𝔽8)11yescharacteristic, complemented
67C7×C13AGL(1,𝔽5)×ΓL(1,𝔽8)11yescharacteristic, complemented
68C4×ΓL(1,𝔽8)—4551no—
69C4×ΓL(1,𝔽8)—4551no—
70C2×C13⋊C3—2451no—
71C7×D5—32no—
72C7×D5C2×#6327011yescharacteristic
73C7×D5C2×#6327111yescharacteristic
74C5×C13C4×#386211yescharacteristic, complemented, Hall
75C3×AGL(1,𝔽5)—6371noHall
76C4×C13—51noHall
77C72AGL(1,𝔽5)×C13⋊C311yescharacteristic, complemented, Sylow
78C2×ΓL(1,𝔽8)—4551no—
79C2×ΓL(1,𝔽8)—4551no—
80C13⋊C3—491noHall
81C5×C7—32no—
82C5×C7C4×#6327011yescharacteristic, complemented
83C5×C7C4×#6327111yescharacteristic, complemented
84C3×D5—6371no—
85C4×C7—51no—
86C4×C7—51no—
87C4×C7—152no—
88C2×C13—51no—
89ΓL(1,𝔽8)—911no—
90ΓL(1,𝔽8)—911no—
91AGL(1,𝔽5)C13⋊#386211yescharacteristic, direct product factor, Hall
92C3×C5—6371noHall
93C2×C7—51no—
94C2×C7—51no—
95C2×C7—152no—
96C13AGL(1,𝔽5)×#386211yescharacteristic, complemented, Sylow
97C3×C4—31851noHall
98D5C2×C13⋊#386211yescharacteristic
99C7—32no—
100C7AGL(1,𝔽5)×#6327011yescharacteristic, complemented
101C7AGL(1,𝔽5)×#6327111yescharacteristic, complemented
102C2×C3—31851no—
103C5C4×C13⋊#386211yescharacteristic, complemented, Sylow
104C4—51noSylow
105C3—6371noSylow
106C2—51no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C72×C13C3×C4
prime radicalD5×C13⋊#3862C2
cosocleC72×D5×C13C2×C3
LCSG ▷ C5×C72×C13
UCSC1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C72×C13×AGL(1,𝔽5)C3semidirect
3. C5×C13⋊#3862C4semidirect
9. C5×C72×C13C3×C4semidirect
14. C13⋊#3862AGL(1,𝔽5)direct (N × H)
16. C7×C13×AGL(1,𝔽5)ΓL(1,𝔽8)semidirect
17. C7×C13×AGL(1,𝔽5)ΓL(1,𝔽8)semidirect
24. C72×AGL(1,𝔽5)C13⋊C3semidirect
30. C72×C13C3×AGL(1,𝔽5)semidirect
36. C5×C7×C13C4×ΓL(1,𝔽8)semidirect
37. C5×C7×C13C4×ΓL(1,𝔽8)semidirect
47. C13×AGL(1,𝔽5)#3862semidirect
48. C5×C72C4×C13⋊C3semidirect
59. C7×AGL(1,𝔽5)#63270semidirect
60. C7×AGL(1,𝔽5)#63271semidirect
66. C7×C13AGL(1,𝔽5)×ΓL(1,𝔽8)semidirect
67. C7×C13AGL(1,𝔽5)×ΓL(1,𝔽8)semidirect
74. C5×C13C4×#3862semidirect
77. C72AGL(1,𝔽5)×C13⋊C3semidirect
82. C5×C7C4×#63270semidirect
83. C5×C7C4×#63271semidirect
91. AGL(1,𝔽5)C13⋊#3862direct (N × H)
96. C13AGL(1,𝔽5)×#3862semidirect
100. C7AGL(1,𝔽5)×#63270semidirect
101. C7AGL(1,𝔽5)×#63271semidirect
103. C5C4×C13⋊#3862semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
D5×C13⋊#38622
C72×C13×AGL(1,𝔽5)3
C4×C13⋊#38625
AGL(1,𝔽5)×#632717
AGL(1,𝔽5)×#632707
AGL(1,𝔽5)×#386213